We consider semidefinite monotone linear complementarity problems (SDLCP) in the space Sn of real symmetric n × n-matrices equipped with the cone Sn+ of all symmetric positive semidefinite matrices. One may define weighted (using any M ∈ Sn++ as weight) infeasible interior point paths by replacing the standard condition XY = rI, r > 0 (that defines the usual central path) by (XY + YX)/2 = rM. Under some mild assumptions (the most stringent is the existence of some strictly complementary solution of (SDLCP)), these paths have a limit as r ↓ 0, and they depend analytically on all path parameters (such as r and M), even at the limit point r = 0.
